ESSAY III - The Structure and Stability of Competitive Dynamical Systems

Abstract

This chapter discusses the structure and stability of competitive dynamical systems. It presents a general framework that encompasses these and many other problems in the theory of economic growth, or more broadly, the theory of economic dynamics. It describes competitive dynamics as Hamiltonian dynamics, where the Hamiltonian can be written as a function of present output prices and current input stocks and can be interpreted as the present value of net national product (equal, by duality, to the present value of net national income). Such a Hamiltonian dynamical system is competitive in the sense that it derives from the perfect-foresight, zero-profit, asset-market clearing equations arising in descriptive growth theory and is consistent with efficiency pricing conditions developed in the Malinvaud tradition and Euler's conditions or, more generally, Pontryagin's maximum principle, applying to production-maximal or consumption-optimal growth problems.